Two consecutive numbers k , k + 1 are removed from 1 , 2 , … , n , reducing the arithmetic mean by 1 . Which statements about n − k are true?

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Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesA.P.Medium2 minQB

MathematicsMediummultiple choice

Two consecutive numbers $k, k + 1$ are removed from $1, 2, \dots, n$ , reducing the arithmetic mean by 1 . Which statements about $n - k$ are true?

Options:(select one or more)

Answer:

B, C

Solution:

The original mean is $(n + 1) /2$ . Equating the new mean to $(n + 1) /2 - 1$ gives $n - k = 1$ . The number 1 is neither prime nor composite and is odd.

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:A.P.

⏱ 2mℹ️ Source: QB

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